Conventionally, the current state of charge of a secondary battery, such as a lead acid storage battery mounted on a car etc. is required to be accurately known. In a secondary battery, in general, since correlation exists between the state of charge and the open-circuit voltage (OCV) in a stable condition, the state of charge may be estimated by calculating the open-circuit voltage. However, the open-circuit voltage of the secondary battery must be measured when charging or discharging is not being performed, and it takes a long time for the open-circuit voltage to be stabilized after charging or discharging is finished. Therefore, various methods for calculating convergence value of the open-circuit voltage have been proposed using the function (voltage characteristic formula) for approximating the time characteristics of the open-circuit voltage (for example, Patent Documents 1 to 3).
In each of the above-described conventional method, the voltage characteristic formula of the open-circuit voltage has an adjustment parameter, and this adjustment parameter is determined by using the measured value of the open-circuit voltage obtained by measuring for a short period of time. And the convergence value of the open-circuit voltage is calculated using the voltage characteristic formula applied with the determined adjustment parameter.
When the convergence value of the open-circuit voltage of the secondary battery is calculated with the above-described conventional method, its precision depends on the precision of the voltage characteristic formula. In general, a polynomial function, a logarithmic function, etc. are used as a voltage characteristic formula; however, since approximating the time characteristics of the open-circuit voltage of the secondary battery with high precision using these functions is difficult, the error of the convergence value of the open-circuit voltage is large.
On the other hand, in the Patent Document 4, a quartic or more exponential attenuation function is used for approximate calculation of the open-circuit voltage of the secondary battery to be able to approximate the open-circuit voltage with high precision and to estimate the state of charge with high precision. In case a complicated nonlinear function such as a quartic or more exponential attenuation function is used for approximate calculation of the open-circuit voltage of the secondary battery, when the adjustment parameter is optimized using a voltage measurement value, the optimum solution of the least-square method must be obtained by solving sequential calculation such as the Gauss-Newton method or the Levenberg-Marquardt method or by performing filtering calculation such as Kalman filter calculation.
Any method described above for optimizing the adjustment parameter has a problem of requiring to set the initial value of the adjustment parameter, and depending on the initial value, the calculation may diverge and the convergence value of the adjustment parameter may not be obtained, or it take extremely long time even when it may be obtained. The Patent Document 4 proposes a method for quickly and stably determining the convergence value of an adjustment parameter.